TORONTO — On the very long list of things we never thought we’d see Bill Murray do in a movie, playing Franklin Delano Roosevelt — at least, playing him straight, without a whiff of “Saturday Night Live”-style spoofing — ranks high. But when “Hyde Park on Hudson” opens later this month (it hits Boston Dec. 14), the quirky performer whose roles have included ghostbuster Peter Venkman and drag queen Bunny Breckinridge will add 32d president of the United States to his resume.

Murray knows what he’s doing. He’s long been a fan of dramatic, left-hand career turns (see “The Razor’s Edge,” Michael Almereyda’s “Hamlet,” “Lost in Translation,” “Broken Flowers”) even when some of those turns haven’t led to success. And he’s just as well known for messing with people offscreen — after almost four decades in the entertainment business he’s still agent-less and infamously hard to pin down or contain.

At the recent Toronto International Film Festival, Murray had a simple request as he ambled into a hotel suite for one of several tightly timed interviews. He wanted water, a cup of coffee, and something to munch on. Specifically, he wanted date bars.

Date bars? Had he confused Canada with Palm Springs? The assembled studio reps looked bewildered, but one of them marched off dutifully and returned a few minutes later with drinks and a plate of pastries — tarts, brownies, éclairs . . . everything but date bars.

“Well, look at you, showing up with that!” Murray said with a warm grin and disproportionate, “What About Bob?”-level enthusiasm. “Thank you!”

Diplomatically sidestepping the dessert issue (do you call that a date detente?), he chugged the coffee and politely requested more. The ensuing interview ranged from collegiate baseball (he’s part owner of the Brockton Rox) to US politics, world history, and abuses of power since the beginning of time. The plate of pastries went untouched.

Nicola Dove/Focus Features

Laura Linney plays Margaret “Daisy” Suckley who has an affair with President Roosevelt, played by Bill Murray.

You get the sense that this is what the White House would be like if Bill Murray really were president. He’s as crafty as he is folksy, and he knows the power of floating an outrageous idea, not because he really expects it to happen but just to see what might come to him as a result. And if “Hyde Park on Hudson” is to be believed, that’s sort of how things were in the FDR White House, too.

Most people know Franklin D. Roosevelt as a man of great wisdom and character, credited with bold New Deal leadership during an era of economic depression and world war. But in Murray’s new movie, directed by Roger Michell (“Notting Hill”) and scripted by Richard Nelson, Roosevelt’s other side — the one that kept up a coldly efficient marriage while he engaged in numerous romantic affairs — takes center stage. The film’s story comes by way of a distant FDR cousin named Margaret “Daisy” Suckley (rhymes with “Bookley’’), whose diary — discovered after her death, in 1991, at 99 — revealed an intimate relationship with the president. As played by Laura Linney, Suckley comes across as naively loyal and groomed to serve, including one very icky scene in Roosevelt’s parked convertible. Murray hopes that scene, extrapolated from what is and isn’t said in Suckley’s journal, isn’t a distraction from what he sees as the larger point and value of both the man and the movie. But even he has trouble reconciling the two sides of the historic hero that “Hyde Park” presents.

“When I first read the script, there was a little bit of, ‘Ohhh [sigh]. Really?’ Maybe that’s my upbringing,” said the Irish-Catholic, Chicago-bred actor. “I’m pretty sure [adultery is] a mortal sin. I have that in my DNA, painted on the walls of my ribs. But I’ve been more influenced by everything else that he did, by everything else he achieved, by the selflessness of the rest of his life.”

Franklin D. Roosevelt Library

President Roosevelt in 1941 with the granddaughter of the caretakers of his cottage retreat near his Hyde Park home.

Murray is no saint. Whether or not you believe his second ex-wife’s allegations of infidelity and abuse, a fair amount of wild and crazy living is on the record. (Let’s just say he wasn’t such an off-the-wall choice to play Hunter Thompson in “Where the Buffalo Roam.”) But at 62 he’s more of a straight arrow than some might guess. That’s why, even after saying he’s made peace with the flawed man at the center of this bio­pic, he later doubles back to admit that he remains conflicted.

“I always have difficulty saying, ‘It’s OK, he can do that ’cause he did a great job with everything else,’” Murray explained. “That’s sort of obviously true but it doesn’t come out of your mouth very easily: Hey, this man devoted his life to public service; he had a dalliance with another woman, or maybe a couple of other women. Is it one of these cognitive things where you go, let’s look at both sides of the ledger? I never felt comfortable with that. That’s sort of not the way I operate.”

It is, however, the type of challenge that can excite an actor and attract other talent in the bargain.

“Bill attempting to play FDR is something that, you know — who wouldn’t want to witness that?” said Linney, 48, of her decision to do the movie, which was filmed largely in London, home to another Hyde Park. “It’s always a fantastic thing to watch someone step outside the zone that people pin on them. If you’re a really good artist, there’s a big range there.”

For Murray, the challenges were physical as well as philosophical. The movie portrays Roosevelt’s paralysis as a daily obstacle surmounted by ingenuity and determination. The actor, whose own sister battled polio, moves around onscreen with the help of crutches, a wheelchair, able-bodied aides, and whatever furniture there is for him to cling to. Murray worked with a voice coach to approximate his character’s peculiar Dutch-influenced, upstate New York accent. Everyone will know it’s still Murray under the pince-nez, but the hope is he’s far enough removed from “Caddyshack,” “Stripes,” and “Meatballs” to make a plausible Roosevelt.

The story zooms in on a period in 1939 when the Roosevelts were visited at their Hyde Park, N.Y., home by England’s King George VI (Samuel West) and Queen Elizabeth (Olivia Colman), who came to cultivate allies in the push toward war. It’s a historical moment that has both weight and lightness to it. Nelson and Michell take ample liberties with the facts, but Murray sees it as a powerful illustration of the kind of open-minded diplomacy that America was built on and needs to rediscover.

“FDR tried everything in his time in office, and often things that were opposite kinds of ideas,” Murray said admiringly. “Someone would have an idea and he would be like, ‘That could work. And that could work.’ There wasn’t a whole lot of blaming going on because we were in a mess. And we’re sort of in a mess now. And if people would cop to their mistakes a little quicker . . . I think people are going to learn how to agree on what we can agree on. I think that’s the new order.”

It sounds like a Zen booster supplement — one that might have helped Murray through his much-talked-about Oscar snub in 2004, when he was the sentimental favorite to take best actor honors for “Lost in Translation” but Sean Penn won instead, for “Mystic River.” Now Murray downplays any talk of awards (“If I have a buzz it’s not from an Oscar, it’s from some sort of dirty drink or something,” he told press in Toronto) and focuses on things that matter a great deal more to him, like his ownership interest in several minor and collegiate league baseball teams, including the Brockton Rox.

“I went this year and saw my first wood bat game and it was joyous,” Murray offered, beaming. “The kids played hard every play; there weren’t like any sluggard pros at the end of their career.”

Next up for Murray: He’s costarring with Charlie Sheen and Jason Schwartzman in the Roman Coppola-directed comedy “A Glimpse Inside the Mind of Charles Swan III,” and down the line there’s the promise of reteaming with “Moonrise Kingdom” director Wes Anderson for “The Grand Budapest Hotel.” One can only imagine the food items he’ll be requesting in Hungary.

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